[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]

*To*: seul-edu@seul.org*Subject*: Re: [seul-edu] [OT] summation of 1/2x*From*: Ray Olszewski <ray@comarre.com>*Date*: Wed, 05 Apr 2000 11:15:31 -0700*Delivery-Date*: Wed, 05 Apr 2000 14:12:16 -0400*Reply-To*: seul-edu@seul.org*Sender*: owner-seul-edu@seul.org

You missed it, jm. The series is easy to sum from 1 to infinity, but impossible to sum from 0 to infinity, since the starting term (1/0) is undefined. I (and others, no doubt) assumed the original posting read 0 due to a typo or a minor slip of the tongue (right, Brian?). Surely this typo is all that Jan was alluding to (otherwise, why the smiley?). And BTW, the sum (from 1 to infinity) is easy to calculate without cutting pieces of paper. Set it equal to X, double it, and subtract the original equation from the doubled one. All the terms cancel out except the leading 2. It's the basic "training wheels" exercise in how to sum an infinite series that converges. In your variant (2 to infinity), the same approach will cause all but the leading 1 to cancel out. And a technical distinction: in math, you can **illustrate** things by cutting up bits of paper, but you cannot **prove** them that way. At 04:25 PM 4/5/00 +0100, jm wrote: > >> > I got to thinking of this last week when a friend and I were trying to >> > remember what the summation of 1/x evaluated from x=0 to x=infinity >> > is. >> >>I would like to see what you found! ;-) > >If I remember well, there is a trick to calculate the sum of 1/2x from 1 to >infinity >you just need a sheet of paper: > + first you cut in half the sheet of paper: you get 1/2 sheet and another >1/2 sheet > + then you cut in half again one of the 1/2 sheet: you get 1/4 and 1/4 >+ then you cut in half again... > >so you can prove that 1/2+1/4+1/8+..+1/2n+.. = 1 ------------------------------------"Never tell me the odds!"--- Ray Olszewski -- Han Solo Palo Alto, CA ray@comarre.com ----------------------------------------------------------------

**Follow-Ups**:**Re: [seul-edu] [OT] summation of 1/2x***From:*bgfay <rid24199@ride.ri.net>

- Prev by Date:
**Re: [seul-edu] [OT] summation of 1/2x** - Next by Date:
**Re: [seul-edu] Intro** - Prev by thread:
**[techentin.robert@mayo.edu: Re: [seul-edu] Long, long ago...]** - Next by thread:
**Re: [seul-edu] [OT] summation of 1/2x** - Index(es):